Seasonal Specific Structural Time Series Models

This paper introduces the class of seasonal specific structural time series models, according to which each season follows specific dynamics, but is also tied to the others by a common random effects. This results in a dynamic variance components model that can account for some kind of periodic behaviour, such as periodic heteroscedasticity, and is tailored to deal with situations when one or a group of seasons behave differently. Trends and non periodic features can be still be extracted and their nature is discussed. Multivariate extensions entertain the case when cointegration pertains only to groups of seasons. We finally show that a circular correlation model for the idiosyncratic disturbances yields a periodic component that is isomorphic to a trigonometric seasonal component.